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We prove that for any affine variety S defined over Q there exist Shephardand Artin groups G such that a Zariski open subset U of S is biregularisomorphic to a Zariski open subset of the character variety Hom(G,PO(3))//PO(3). The subset U contains all real points of S . As an applicationwe construct new examples of finitely-presented groups which are notfundamental groups of smooth complex algebraic varieties.

On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties